Question 1187171
the x-intercept is the value of x when the value of y = 0.


the equation is f(x) = 4 * |x - 3| - 1.
set y = f(x) and the equation becomes y = 4 * |x - 3| - 1.
set y equal to 0 and the equation becomes 0 = 4 * |x - 3| - 1.
this is the same as 4 * |x - 3| - 1 = 0.
add 1 to both sides of the equation to get 4 * |x - 3| = 1.
divide both sides of the equation by 4 to get |x - 3| = 1/4.
when the expression within the absolute value sign is positive, the equation becomes x - 3 = 1/4.
add 3 to both sides to get x = 3 + 1/4 = 13/4.
when the expression within the absolute value sign is negative, the equation becomes -(x-3) = 1/4.
simplify to get -x + 3 = 1/4
subtract 3 from both sides to get -x = -3 + 1/4
multiply both sides by -1 to get x = 3 - 1/4 = 2 + 3/4 = 11/4.


the x-intercept should be x = 11/4 or and x = 13/4.


when x = 11/4, the equation becomes f(x) = 4 * abs(11/4 - 3) - 1 which becomes f(x) = 4 * abs(11/4 - 12/4) - 1 which becomes f(x) = 4 * 1/4 - 1 which becomes f(x) = 0.
when x = 13/4, the equation becomes f(x) = 4 * abs(13/4 - 3) - 1 which becomes f(x) = 4 * abs(13/4 - 12/4) - 1 which becomes f(x) = 4 * 1/4 - 1 which becomes f(x) = 0.


both values of x are confirmed to be good.


your solution is that the y-intercepts are at x = 11/4 and x = 13/4.


abs(x-3) means the same thing as |x-3|.


the equation was graphed and is shown below.


<img src = "http://theo.x10hosting.com/2021/110302.jpg" >


11/4 = 2.75 as shown on the graph.
13/4 = 3.25 as shown on the graph.